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We study graphene with an adsorbed spin texture, where the localized spinscreate a periodic magnetic flux. The latter produces gaps in the graphenespectrum and breaks the valley symmetry. The resulting effective electronicmodel, which is similar to Haldane's periodic flux model, allows us to tune thegap of one valley independently from that of the other valley. This leads tothe formation of two Hall plateaux and a quantum Hall transition. We discussthe density of states, optical longitudinal and Hall conductivities for nonzerofrequencies and nonzero temperatures. A robust logarithmic singularity appearsin the Hall conductivity when the frequency of the external field agrees withthe width of the gap.

Valley symmetry breaking and gap tuning in graphene by spin doping